4x-1=-9(1/3x+4)

Solution for 4x-1=-9(1/3x+4) equation:

4x-1=-9(1/3x+4)

We move all terms to the left:

4x-1-(-9(1/3x+4))=0


Domain of the equation: 3x+4))!=0

x∈R


We multiply all the terms by the denominator


4x*3x-1*3x+4))-(-9(1+4))=0

We add all the numbers together, and all the variables

4x*3x-1*3x+4))-(-95)=0

We add all the numbers together, and all the variables

4x*3x-1*3x=0

Wy multiply elements

12x^2-3x=0

a = 12; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·12·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*12}=\frac{6}{24}
=1/4
$